%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode

\documentclass[11pt,tikz,border=1]{standalone}
\usetikzlibrary{calc,positioning}
\usepackage{pgfplots}

\usepackage{cjkfonts}

\begin{document}

  \begin{tikzpicture}

      \begin{axis}[
          width=7cm,
          height=7cm,
          xlabel={\normalsize $x$},
          axis lines=center,
          tick label style={font=\tiny},
          label style={font=\tiny},
          title style={font=\scriptsize},
          xtick={1},
          ytick={-2,-1,0,1,2},
          % minor tick num=1,
          title={$\sigma^{-1} \circ f(x)$},
          declare function={
            sigmaInverse(\z)=ln(\z/(1-\z));
            f(\x)=0.2+0.4*\x*\x+0.3*\x*sin(15*deg(\x))+0.05*cos(50*deg(\x));
          },
        ]
        \addplot[blue,domain=0:1,samples=201] {
          sigmaInverse(f(x))
        };
      \end{axis}

  \end{tikzpicture}

\end{document}
